Suppose that $$ 64 \% $$ of students in a college have a smart phone. If you select three students at random, what is the probability that all three have a smart phone? Write the probability as a decimal rounded to three decimal places.

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We start by noting that the probability that one student has a smart phone is $$0.64$$. Since we select three students independently, the probability that all three have a smart phone is:

$$
0.64^3 = 0.64 \times 0.64 \times 0.64
$$

Calculating step-by-step:

1. First, compute $$0.64 \times 0.64$$:

$$
0.64 \times 0.64 = 0.4096
$$

2. Then multiply the result by $$0.64$$:

$$
0.4096 \times 0.64 = 0.262144
$$

Rounded to three decimal places, the probability is:

$$
0.262
$$

Thus, the final answer is $$0.262$$.
The probability that all three students have a smart phone is 0.262.

Suppose that of students in a college have a smart phone. If you select three students at
random, what is the probability that all three have a smart phone?
Write the probability as a decimal rounded to three decimal places.

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Suppose that of students in a college have a smart phone. If you select three students at random, what is the probability that all three have a smart phone? Write the probability as a decimal rounded to three decimal places.